Proof By Contradiction - Calculus Based Example

[pouchmaster69]

PatrickJMT, helping me in through my calculus classes, and now helping me with my discrete math class. You sir, are a jack of all trades.

[patrickJMT]

@pouchmaster69 i always really liked the discrete stuff, i should do more videos on it

[DulinJD]

@patrickJMT I think all students in discrete classes would agree. Thanks for all of your videos!

[ownedaxis]

@patrickJMT absolutely. In my opinion, discrete stuff is way harder than the calculus, mostly because you don't have videos about discrete math. :-)

[patrickJMT]

@ownedaxis ha :) only a few

[grlaer]

What about the use of Rolle's theorem? Where does that come into play?

[JThorss0N]

Great explanation! I think c should be in the open interval (r1,r2) though, because in both Rolle's theorem and the Mean value theorem you're assuming f is continuous in the closed interval [a,b] and differentiable in the open interval (a,b).

[arsenalwak]

2.. 3.. 20 times, haha what a legend ;)

[Stavers50]

you're left-handed too! Makes you even cooler

[duhboss1]

I really like this video. You do a solid job of showing what a powerful tool calculus can be.

[sugarcoatedsour]

It would have been better to use Rolle's Theorem since you are looking for roots, because Rolle's theorem specifically states that f'(c')=0 and since the derivative of the given function is never less than 2, it would be a contradiction. IMHO.

[fakwater]

I bought your Itouch app for calc 1 and was looking for some examples such as these, do you think you will link them up any time soon? BTW I stopped going to my math class because I learn more off your videos then i do in class. I currently have a B in my class.

[mudgalsourabh348]

its a pretty nice way of solving a mathematical problem

[XTC2525]

I would've never thought to use calc theorems to solve this lol the 1st think I thought to do was just just plug in 2 arbitrary roots to the function set the functions equal to each other and show that your roots would have to be equal. I've been watching a number of your vidz lately and I like how you use different means to arrive at the correct answer, this helps me when I tutor people

[osamabinladin4u]

thanks patrick. you should be paid for these vids

[TheTriSarahTops]

Oh hell yes that is THE problem I just worked!! But I needed to actually understand the significance of the contradiction, so thanks!

[hamzahamid7]

awesome video. thanks man

[riukio1340]

This is some good stuff my teacher has a weird attitude or it the lighting in her class room because my entire class is getting a C+ no lower or higher its probably something shes not doing correctly

[valsera246]

I don't know what I would do without your videos! You are the best :) Thanks a million!

[BLAKEBOFFA]

Patrick, you got me through Calc 1, 2 and 3. It's been a while since I've watched your videos. I'm struggling in Advanced Calc now and this has been very helpful. Thank you so much for everything!

[Joojoo600]

at the beginning when u used the IVT, how did u know to plug in 0 and -1 to find that the polynomial has 1 root?

[coolkid19901]

How could you have graphed it as if you knew it would look like that at 8:18? Because it seems that based on this graph (that you drew out of thin air) that you can assume that f'(c) = 0 what if the graph looked different? Because of the maxima of the graph which has a slope equalling to the x-axis? Please respond someone!

[coolkid19901]

@coolkid19901 Nevermind its because your assuming that there are two roots being endpoints thus you have to look for something that is parallel to that which is 0 in this case!!

[aznbubba77]

when assuming there are 2 roots, could you also have used rolle's theorem to prove that there is a contradiction?

[geovaniluna]

Thanks man. Very Helpful.

Once again. Thanks Really appreciate what you do.

[Nifardeen]

Thanks patrick, you absolutely make calc so much more easier to understand. I truly appreciate your help. Hope you keep up the good work. Thanks once again.

Regards.

[hmoobdaj]

wow

this is the same exact problem (numbers and everything) that was in the book....

[zeiontic]

How did you know to pick -1 and 0 for the intermediate value system?

[HCI344]

He just tried 2 arbitrary number, normally it is easy to start with 0, 1, -1, 2, -2, ... and see if it gives us positive or number values for Y

[webmastertool]

@zeiontic It's basically Guess And Check by picking points that would interest the function ie look at the domain and range and pick appropriate points.

[davidfournier25]

@zeiontic

Unfortunately, you just gotta use intuition...in other owrds, guess at it. In the end however, you wanna have the result of your f(a) be of opposite polarity of f(b). In the video, his f(a)=1 and the f(b)=-6, see, opposite polarity :-)

[abuccilli]

Now that you have completed the problem and explained it logically, you should write the proof out, as if you were going to submit it for homework or it was going to be published.

[duyu]

My appreciation for your videos can be contradicted by nothing!

[Morgfang]

It's pronounced like "rollz" ;)

[tombert256]

This is pretty cool. I've always wanted to learn how to do these types of proofs...they seem to breeze over these things in my calc classes.

I like all your videos. They can be extremely helpful, and honestly, they are somewhat pleasant to watch.

[patrickJMT]

who'da thunk?

math, pleasurable....

[tombert256]

I told my calc BC class about you a few days ago, since we were all having a bit of trouble with finding the radius and endpoints of convergence.

I don't know if your videos helped them, but I have no reason to think they wouldn't.

[patrickJMT]

well hopefully i did not make them more clueless at least : )

[Spiderboydk]

Good explaination, but the proof can be made much simpler with a direct approach (f'(x) >= 2 implies f strictly increasing everywhere implies at most 1 root). I know it's done this way for the sake of explaination of contradiction proofs, but I just wanted to let people know this problem can be solved simpler.

[patrickJMT]

yep, for sure!

but as you pointed out, i am trying to make the idea of 'proof by contradiction' easy to understand.

[friendlyfire53]

Nice video, but no high def?

[patrickJMT]

yes, is available in hd.

when i first post them, they appear for a few minutes without the hd feature for some reason

[friendlyfire53]

Oh that's weird. Thanks!

[Spiderboydk]

That is because Youtube has to trancode your video.

It first transcode a low quality version because it's quick and the video becomes available soon after upload. It later transcode a higher quality version.